Kernel modeling for molecular surfaces using a uniform solution

In this paper, a rational Bezier surface is proposed as a uniform approach to modeling all three types of molecular surfaces (MS): the van der Waals surface (vdWS), solvent accessible surface (SAS) and solvent excluded surface (SES). Each molecular surface can be divided into molecular patches, which can be defined by their boundary arcs. The solution consists of three steps: topology modeling, boundary modeling and surface modeling. Firstly, using a weighted @a-shape, topology modeling creates two networks to describe the neighboring relationship of the molecular atoms. Secondly, boundary modeling derives all boundary arcs from the networks. Thirdly, surface modeling constructs all three types of molecular surfaces patch-by-patch, based on the networks and the boundary arcs. For an SES, the singularity is specially treated to avoid self-intersections. Instead of approximation, this proposed solution can produce precise shapes of molecular surfaces. Since rational Bezier representation is much simpler than a trimmed non-uniform rational B-spline surface (NURBS), computational load can be significantly saved when dealing with molecular surfaces. It is also possible to utilize the hardware acceleration for tessellation and rendering of a rational Bezier surface. CAGD kernel modelers typically use NURBSs as a uniform representation to handle different types of free-form surface. This research indicates that rational Bezier representation, more specifically, a bi-cubic or 2x4 rational Bezier surface, is sufficient for kernel modeling of molecular surfaces and related applications.

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